Suppose that the production function is f(x₁, x₂)=(x^a₁ +x^a₂)b, where a and b are positive constants.For what values of a and b is there a diminishing technical rate of substitution? A)For any value of a if b

Question

Suppose that the production function is f(x₁, x₂)=(x^a₁ +x^a₂)b, where a and b are positive constants.For what values of a and b is there a diminishing technical rate of substitution? A)For any value of a if b < 1 B)For any values of a and b if ab < 1 C)For any values of a and b if a > b D)For any value of b if a < 1 E)None of the above.

Quizplus · Accepted Answer

The technical rate of substitution between the inputs x₁ and x₂ is given by the partial derivative of f with respect to x₁ divided by the partial derivative of f with respect to x₂. That is, RTS=S1S1S1S1F1F1F1S1S1S1S1(x^a₁ F1F1F1S1S1S1S1F1F1F10 x^a₂)b 􀂒􀂒􀂒􀂎􀂒􀂒􀀃= F1F1F1S1F1F1F1S1{x^a₁ [x^a₂]b-1}􀀄􀀃􀀷􀀷􀀷􀀃􀀷􀀷􀀷􀀃􀀷􀀷􀀷􀀃􀀷􀀷􀀷􀀃􀀷􀀷􀀷􀀃􀀷􀀷􀀷􀀃􀀷􀀷􀀷􀀄􀀃 The RTS decreases as x₁ increases and x₂ decreases when the quotient inside the braces is less than 1. Therefore, we need: x^a₁ [x^a₂]b-1

Suppose That the Production Function Is F(x1, X2)=(xa1 +Xa2)b, Where

Suppose That the Production Function Is F(x₁, X₂)=(x^a₁ +X^a₂)b, Where